Question

Solve the following equation giving your answers in terms of natural logarithms
$4\cos hx+\sin hx=4$

Answer 1

$4\cos hx+\sin hx=4$

$4\left(\frac{e^x+e-x}{2}\right)+\frac{e^x-e^{-x}}{2}=4$

$5e^{2x}-8e^x+3=0$

$e^x=\frac{3}{5}$ or $1$

$x=log\left(\frac{3}{5}\right)$ and $1$